Problem: Simplify the following expression: $\sqrt{112}-\sqrt{7}+\sqrt{28}$
Answer: First, try to factor any perfect squares out of the radicals. $= \sqrt{112}-\sqrt{7}+\sqrt{28}$ $= \sqrt{16 \cdot 7}-\sqrt{7}+\sqrt{4 \cdot 7}$ Separate the radicals and simplify. $= \sqrt{16} \cdot \sqrt{7}-\sqrt{7}+\sqrt{4} \cdot \sqrt{7}$ $= 4\sqrt{7}-\sqrt{7}+2\sqrt{7}$ Finally, simplify by combining the terms. $= ( 4 - 1 + 2 )\sqrt{7} = 5\sqrt{7}$